walker wrote:
Let's move from one coin to another:
1) m1 = 30 g.
2) decrease in thick from 2mm to 1mm: m = 30 * 1/2
3) increase in diameter from 15mm to 30mm: m= 30 * 1/2 * 2^2
4) substitute 1/2 of silver to 1/2 of aluminum: it reduces weight by 3/2 times: m = 30 * 1/2 * 4 * 2/3 = 40 g.
You make it look so simple but I am afraid I did not get the tail or head of what you tried to explain.
How are you relating weight thickness and diameter? In 2 Are you saying that as thickness decreases weight also decreases and hence divide by 2??
Diameter increased by 2 but why are you multiplying by 2^2 rather than 2? Is it because to account for 2 sides of coin?
What really perplexed me is this Sentence
The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver.
Can you explain why the weight reduces by 3/2 times? It is talking about weight of the coin and then says volume of AL and Si are same. Its not like they are 15 gms each.
Here is the OE and OA
Denote S the weight of silver and A the weight of aluminum in the first coin. We can compose an equation: S + A = 30 or 2A + A = 30. Thus, the aluminum half of the coin weighs 10 grams. If the coin were made of pure aluminum, the second half of the coin would also weigh 10 grams and the whole coin would weigh 20 grams.
If we look at the proportions of the second coin, we will see that it is twice as large as the first coin
(volume2 = \(1(\frac{30}{2})^2 \pi\) ; volume1 = \(2(\frac{15}{2})^2 \pi)\) . The second coin were made of pure aluminum would be twice as heavy as the first coin made of pure aluminum. The answer to the question is therefore 20*2 = 40 grams.
The correct answer is B.
While the OE makes a lot of sense in the first part, I dont understand what kind of an object are they considering the coin to be? Sphere?